Chapter 8, Problem 4CCSR

To determine

Towrite:The letter of the correct answer.

Answer to Problem 4CCSR

The option I is correct.

Explanation of Solution

Given information:

The area of a rectangle is $6n^2+n-2$ . Which expression could represent the perimeter of the rectangle?

F. $2n-1$G. $3n+2$H. $5n+1$I. $10n+2$

Conceptused:

The area A of a rectangle is given by $A=l\times w$ , where l and wrespectively are the length and width of the rectangle.

Calculations:

The area of the rectangle is $A=6n^2+n-2$ that may be written as a product of factors as

  $A=6n^2+4n-3n-2$$\because 6\times -2=-12=4\times -3$

  $\Rightarrow A=2n\left(3n+2\right)-1\left(3n+2\right)$

  $\Rightarrow A=\left(3n+2\right)\left(2n-1\right)$

Since, $\left(3n+2\right)>\left(2n-1\right)$ therefore, $\left(3n+2\right)$ is the length of the rectangle and $\left(2n-1\right)$ the width.

Therefore, the perimeter of the rectangle is $P=2\left(l+w\right)=2\left(3n+2+2n-1\right)$

  $\Rightarrow P=2\left(5n+1\right)=10n+2$

Hence, the option I is correct.

Conclusion:

The option I is correct.